A mineral is commonly defined as a naturally occurring crystalline solid in the current art. In this document, the definition of a mineral is extended to also comprise a synthetic crystalline solid which would be defined as a mineral in the common sense if it had occurred naturally.
The density of a mineral is defined as the mass of a mineral divided by the total volume of the mineral. The density of apatite minerals studied by human beings lies within the range 3.16-3.22 grams per cubic centimeter. The density of most zircon minerals studied by human beings lies within the range 4.6-4.7 grams per cubic centimeter.
In chemistry, concentration is commonly defined in the current art as the abundance of a constituent divided by the total volume of the mixture containing that constituent. Alternatively, concentration may be defined as the mass of a constituent divided by the total mass of the mixture containing that constituent. For mineral species, it is common practice in the current art to express concentration in units of weight percent; weight percent is the percent of the total mass of the mixture represented by the mass of the constituent; comparing concentrations in units of weight percent of an element from mineral to mineral of the same species assumes essentially constant density among the same minerals. For mineral species, it is also common practice in the current art to express concentration in terms of parts per million; parts per million is the number of micrograms of constituent contained in one gram of mixture; comparing concentrations in units of parts per million of an element from mineral to mineral of the same species assumes essentially constant density among the same minerals. For mineral species, it is also common practice in the current art to express concentration in units of atoms per formula unit; atoms per formula unit is the number of atoms of a constituent in the chemical formula of a mixture.
In the current art, chemical elements may be represented by chemical symbols commonly listed in the periodic table of the chemical elements. Symbols for chemical elements used in this description of the preferred embodiment of the invention include: Ca for the element calcium; P for the element phosphorus; O for the element oxygen; F for the element fluorine; Cl for the element chlorine; Zr for the element zirconium; Si for the element silicon; Ar for the element argon.
The most common natural occurrences of the mineral apatite studied by human beings have chemical compositions represented by the chemical formula Ca10(PO4)6[F,Cl,OH]2, The most common natural occurrences of the mineral apatite studied by human beings also comprise a range of fluorine, chlorine, and OH combinations. These natural apatite minerals comprise a range of various detectable and minor elements including: iron, manganese, and cerium, samarium, and other rare earth elements substituting for calcium; aluminum, silicon, sulfur, and arsenic substituting for phosphorous; bromine substituting for fluorine, chlorine, and OH. Most naturally occurring apatite minerals also contain detectable amounts of lead, thorium, and uranium.
The most common natural occurrences of the mineral zircon studied by human beings have chemical compositions represented by the chemical formula Zr4(SiO4)4. These natural zircon minerals comprise a range of various detectable and minor elements including: hafnium, and cerium, samarium, and other rare earth elements substituting for zirconium; aluminum substituting for silicon. Most naturally occurring zircon minerals also contain detectable amounts of lead, thorium, and uranium.
Each atomic nucleus of an element is composed of a fixed number of protons specific to that element. As an example, each uranium atomic nucleus contains 92 protons. Each element is also composed of one or more isotopes. The atomic nucleus of each specific isotope of an element is composed of a fixed number of protons specific to that element and a fixed number of neutrons specific to that isotope of that element. An atomic nucleus of the isotope 235U contains 92 protons and 143 neutrons; the superscript 235 preceding the chemical symbol U indicates the sum of the number of protons and neutrons for the isotope 235U. An atomic nucleus of the isotope 238U contains 92 protons and 146 neutrons.
Isotopes of lead, thorium, and uranium in a natural apatite or zircon mineral may be used to study the natural history of the apatite or zircon mineral. Each 235U atomic nucleus possesses an inherent probability that it will undergo spontaneous radioactive decay by emission of a 4He nucleus. Emission of a 4He nucleus by an atomic nucleus is a process commonly referred to as alpha-decay in the current art. Each 235U atomic nucleus that experiences alpha-decay is transmuted to a single 207Pb atomic nucleus and seven 4He atomic nuclei. Each 238U atomic nucleus possesses an intrinsic probability that it will undergo alpha-decay and be transmuted to a single 208Pb atomic nucleus and eight 4He atomic nuclei. Each 232Th atomic nucleus possesses an intrinsic probability that it will undergo alpha-decay and be transmuted to a single 208Pb atomic nucleus and six 4He atomic nuclei. Immediately following each emission of a 4He atomic nucleus, the 4He atomic nucleus is repelled from its parent atomic nucleus and it leaves a zone of damaged host crystal along its path of travel. For each emission of a 4He atomic nucleus, the resulting zone of damaged host crystal left by the 4He atomic nucleus is commonly referred to as a latent alpha track in the current art.
Each 238U atomic nucleus possesses an inherent probability that it will undergo spontaneous radioactive decay by nuclear fission. Nuclear fission is a process by which the atomic nucleus undergoing fission splits into two or three nuclear particles, each particle larger than a 4He atomic nucleus. Immediately following nuclear fission, the resultant nuclear particles repel each other, the nuclear particles travel in opposing directions within their host crystal lattice, and the nuclear particles leave zones of damaged host crystal along their paths of travel. For each single nuclear fission event, the sum of the resulting zones of damaged host crystal left by the two or three nuclear particles is commonly referred to as a latent fission track in the current art.
Several methods of the current art utilize measurements of the relative abundances of one or more isotopes of lead, thorium, and uranium, and/or samarium, the relative abundance of the isotope 4He, and/or the relative abundance of latent fission tracks within a natural apatite or zircon mineral. As an example, knowledge of the relative abundances of the isotopes 238U and 206Pb within a natural zircon mineral may be used to calculate the time elapsed since the zircon mineral crystallized. The current art method commonly referred to as uranium-lead dating comprises this approach; uranium-lead dating may be applied to other minerals such as apatite in the current art. Accurate and precise uranium-lead dating of a natural zircon mineral may also comprise the measurement of the relative abundances of the isotopes 207Pb, 208Pb, 232T, and 235U to enable the human being to more fully comprehend the implications of the measurements of the relative abundances of 206Pb and 238U. As another example, knowledge of the relative abundances of the isotopes 147Sm, 232Th, 235U, 238U and 4He within a natural zircon mineral may be used to calculate the time elapsed since 4He effectively ceased to diffuse out of the zircon mineral. The current art method commonly referred to as uranium-thorium-samarium-helium dating comprises this approach; uranium-thorium-samarium-helium dating may be applied to other minerals such as apatite in the current art.
Several methods of the current art utilize measurements of the concentrations of elements in minerals. As an example, consider a case in which a natural zircon mineral is derived from a rock comprised of sand deposited by a river. In this case, there may exist one or more populations of individual zircon minerals mixed together within this sand if the river that transported and deposited the sand also transported and deposited zircon minerals from one or more upstream or airborne sources. A detailed understanding by the human being of the concentrations of detectable and minor elements within each zircon mineral from the mixture of zircon minerals may enable to human being to group the zircon minerals into their respective populations.
Following the nuclear fission of a 238U atomic nucleus in apatite, the damaged host crystal lattice that comprises the resultant latent fission track begins to spontaneously and irreversibly convert back to undamaged host crystal lattice by a process referred to annealing in the current art. A latent fission track in apatite may be preferentially dissolved using an appropriate chemical mixture and studied by a human being. The study of chemically dissolved latent fission tracks in apatite is commonly referred to fission track analysis of apatite in the current art. Based on studies of apatite minerals chosen by human beings to represent the most common natural occurrences of the mineral apatite, the current art comprises knowledge of the rate of conversion of the damaged host crystal lattice comprising a latent fission track back to undamaged host crystal lattice including: the rate increasing with increasing temperature; the rate increasing with increasing fluorine concentration in the host apatite mineral; the rate decreasing with increasing chlorine concentration in the host apatite mineral; the rate likely decreasing with increasing iron concentration in the host apatite mineral; the rate likely decreasing with increasing manganese concentration in the host apatite mineral; the rate likely decreasing with increasing cerium and other rare earth element concentrations in the host apatite mineral. A detailed understanding by the human being of the concentrations of detectable and minor elements within each apatite mineral from which measurements pertaining to dissolved latent fission tracks are derived may enable to human being to better interpret the measurements pertaining to the dissolved latent fission tracks.
One common method in the current art of determining the concentration of an element in a mineral of interest is commonly referred to as electron probe microanalysis. Electron probe microanalysis of the concentration of a specific element in a mineral of interest comprises: focusing a beam of electrons onto a surface of the mineral of interest; detecting x-ray radiation that results from the interaction of the electrons with atoms in the mineral of interest; seeking and counting x-rays of a specific energy that are diagnostic of the specific element; comparing the count of x-rays of this specific energy from the mineral of interest to the count of x-rays of the same specific energy generated from a reference material containing the specific element at a known concentration; converting the x-ray count for the specific element from the mineral of interest to the concentration of the specific element in the mineral of interest. Comparing x-ray counts between the mineral of interest and the reference mineral requires the generation of the x-rays under a constant set of operating conditions comprising: essentially equal electron beam current and potential; essentially equal environment at the surface where the electron beam intersects the mineral of interest and the reference mineral. The reference material used in electron probe microanalysis in the current art may be of the same mineral species as the mineral of interest or it may be a mineral of a different species or a material that is not a mineral such as a synthetic glass.
A second common method in the current art of determining the concentration of an element in a mineral of interest is commonly referred to as laser ablation-mass spectrometry. Laser ablation-mass spectrometry measurement of the concentration of a specific element in a mineral of interest comprises: focusing a beam of photons onto a surface of the mineral of interest causing the mineral of interest to be fragmented; transporting fragments of the mineral of interest into a mass spectrometer; seeking and counting an isotope that is diagnostic of the specific element; comparing the count of the isotope specific to the element from the mineral of interest to the count of the same isotope generated from a reference material containing the specific element at a known concentration; converting the isotope count for the specific element from the mineral of interest to the concentration of the specific element in the mineral of interest. Comparing isotope counts between the mineral of interest and the reference mineral requires the generation of fragment of the mineral of interest fragments and fragments of the reference mineral under a constant set of operating conditions comprising: essentially equal photon beam frequency and intensity; essentially equal fragment generation rate resulting from the interaction with the photon beam; essentially equal transport rate of the fragments to the mass spectrometer. The reference material used in laser ablation-mass spectrometry in the current art may be of the same mineral species as the mineral of interest or it may be a mineral of a different species or a material that is not a mineral such as a synthetic glass.
A case may be encountered in the current art of laser ablation-mass spectrometry wherein the rate of generation of fragments of the mineral of interest differs from the rate of generation of fragments of the reference mineral when all attempts are made by a human being to avoid this difference. One such case exists when photons fragment the surface of a zircon mineral containing latent alpha tracks and isotope counts from these fragments are compared to isotope counts from a reference mineral that lacks latent alpha tracks. The latent alpha tracks in the zircon mineral of interest render the crystal lattice of the zircon mineral of interest softer than its pristine counterpart and thereby enhance the rate of fragmentation by the photons relative to the rate of fragmentation by the photons of its pristine counterpart. The rate of fragmentation by photons among zircon minerals may commonly vary because the number of latent alpha tracks among zircon minerals commonly varies. A second such case exists when photons fragment the surface of an apatite mineral of interest containing dissolved latent fission tracks and isotope counts from these fragments are compared to isotope counts from fragments of a reference mineral that lacks dissolved latent fission tracks. The dissolved latent fission tracks in the apatite mineral of interest enhance the rate of fragmentation by the photons relative to the rate of fragmentation by photons of an apatite mineral containing zero dissolved latent fission tracks. The rate of fragmentation by photons among apatite minerals may commonly vary because the number of dissolved latent fission tracks per unit volume of fragmented apatite mineral among apatite minerals commonly varies. A third such case exists when the rate of transport to the mass spectrometer of fragments of the mineral of interest or fragments of the reference mineral depends on the position of the mineral of interest or reference mineral within the fragmentation apparatus. It is common in the current art for transport rate to vary from within the fragmentation apparatus due to variable flow of the transport gases within the fragmentation apparatus comprising the current art. These three cases may exist alone or in some combination together.